Inventory Routing Problem Research Articles

Robust optimization approaches for the perishable product inventory routing problem with demand uncertainty

Robust optimization approaches for the perishable product inventory routing problem with demand uncertainty

Design of Multi-Period Inventory Routing Problem Considering Road Rehabilitation Plans in Post-Disaster

Design of Multi-Period Inventory Routing Problem Considering Road Rehabilitation Plans in Post-Disaster

Inventory management and delivery of perishable products with stochastic demands and risks consideration

In the agri-food supply chain, the perishable nature of the commodities opens a series of challenges at all decision levels: strategical, tactical and operational. This paper presents an age-based model for the inventory-routing problem of perishable commodities with stochastic demands. To deal with this source of uncertainty, the conditional value-at-risk (CVaR) has been adopted as a risk measure, and then the model has been applied to the agri-food supply chain under investigation. The model is the core of a dynamic approach for the optimal distribution and inventory planning over a short-medium horizon. To address a problem as realistic as possible, we assume that the demand for products of each age is unknown and we model this uncertainty by means of random variables with a probability distribution that can be estimated from historical data. Computational experiments on test cases based on a real-life agri-food company located in Italy show the effectiveness of the proposed approach for evaluating different risk attitudes.

Stochastic inventory routing with dynamic demands and intra-day depletion

Businesses such as supermarkets face an inventory routing problem with distinct stochastic dynamic demand distributions for various weekdays and times of the day. Most research, however, considers aggregated per-period demand and inventory depletion, thereby oversimplifying actual events. We formulate the problem as a finite-horizon stochastic dynamic program that accounts for the dynamic demand throughout the planning horizon and within each planning period. The models include different levels of information aggregation to decide the replenishment quantities and times by dividing periods into sub-periods with distinct demand distributions. This division helps the supplier create efficient replenishment plans and account for intra-day inventory levels. The modeled characteristics include routing, holding and stock-out costs, delivery time windows, inventory and vehicle capacities, and delivery time windows. The problem is solved using an iterative lookahead algorithm with an adaptive large neighborhood search for the routing and policy learning for the replenishment decisions. Numerical evaluations show the benefit of intra-day planning, effects of instance sizes, different coefficients of variation, and holding costs compared to benchmark replenishment policies. Considering intra-day depletion and demand data for each sub-period helps achieve savings of more than 20% compared to planning for full periods. The savings are obtained by adjusting delivery quantities, incorporating intra-day consumption, creating more efficient delivery routes, and correctly timing replenishments.

A goal programming model for the stability analysis of a maritime inventory routing replanning problem

This paper aims to provide insight into the stability of solutions to a multi-product maritime inventory routing problem (MIRP) when replanning due to the occurrence of unexpected events. The MIRP determines vessel routes while ensuring that port inventory levels remain within operational thresholds. In today's global economy, supply chains are often vast and complex. Managing inventory and routes for multiple products across international waters is a daunting task. The MIRP provides a framework for optimizing these complex supply chain networks. Four stability metrics are available to evaluate the stability of the adjusted plans. The problem is modeled using a goal programming approach to consider all stability metrics simultaneously. Then, 30 instances from the literature are solved using CPLEX. It is shown that there are significant differences when all stability metrics, as opposed to a single one, are considered simultaneously, which can lead to better agreement between the vendor and the retailer in decision making. A cost analysis is performed to examine the impact of the cost increase on the stability of the other metrics. The key finding is that when all stability metrics are considered simultaneously, a 5 % increase in cost can result in 7.5 % fewer changes to replanned solutions, while this rate is less than half when the stability metrics are considered individually. This highlights the significance of evaluating all metrics simultaneously instead of analyzing each metric separately.

Closed-loop inventory routing problem for perishable food with returnable transport items selection

Urged by the necessity to establish sustainable supply chains (SCs), this study focuses on exploring the closed-loop inventory routing problem (CIRP) for perishable food packed by multi-type returnable transport items (RTIs). The selling revenue of perishable food is dependent on food's remaining shelf life and the specific type of RTIs used for packaging. RTI selection decisions need to be jointly considered in the CIRP to weigh the potential benefits against associated costs. For this problem, we first develop an integer linear programme (ILP) to maximise the total profit of the holistic SC. Subsequently, we design a tailored kernel search (KS) matheuristic as an efficient solution. A real CIRP with multi-type RTIs for fresh strawberries is used to demonstrate the practicality of the ILP. For this case study, we perform extensive sensitivity analysis of the relevant parameters, extracting valuable managerial insights. Finally, experiments are conducted on 170 randomly generated instances. Computational results show that the proposed KS manages to achieve competitive solutions for instances with up to 10 retailers much more efficiently than CLPEX. For instances with up to 40 retailers, the KS algorithm significantly outperforms CPLEX in terms of solution quality, improving the obtained profit by 80.03% on average under the same computational time.

Solving a Continent-Scale Inventory Routing Problem at Renault

This paper is the fruit of a partnership with Renault. Their reverse logistic requires solving a continent-scale multiattribute inventory routing problem (IRP). With an average of 30 commodities, 16 depots, and 600 customers spread across a continent, our instances are orders of magnitude larger than those in the literature. Existing algorithms do not scale, so we propose a large neighborhood search (LNS). To make it work, (1) we generalize existing split delivery vehicle routing problems and IRP neighborhoods to this context, (2) we turn a state-of-the-art matheuristic for medium-scale IRP into a large neighborhood, and (3) we introduce two novel perturbations: the reinsertion of a customer and that of a commodity into the IRP solution. We also derive a new lower bound based on a flow relaxation. In order to stimulate the research on large-scale IRP, we introduce a library of industrial instances. We benchmark our algorithms on these instances and make our code open source. Extensive numerical experiments highlight the relevance of each component of our LNS. Funding: This work was supported by Renault Group. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0342 .

Optimizing a Multi Period Deterministic Inventory Routing Problem in Agriculture Industries

This paper develops a solving model for multi-period deterministic inventory routing problem (MP-DIRP) in supply chain focus on agriculture industries. The issue is how to improve the perishable product delivery process from a distribution centre (DC) to a collection of customers over a planning horizon. This paper proposed a model to achieve optimization in terms of costs respectively. The transportation problem is solved by using a simulation technique and developed using an algebraic modelling language which is known as a mathematical programming language (AMPL) to find an optimal solution within the period. The route for a distribution centre (DC) is set up by a supplier depending on the number of products assigned to each customer, which contributes to determining the best inventory routing problem (IRP) for each period. As a result, by applying the transportation model developed in this study, it is expected that the industries can achieve optimization by minimizing their total inventory and transportation costs.

A GIS-based maritime supply chain network design of distant-water fisheries

In the pursuit of efficient and cost-effective supply chain management within the marine capture fishery sector, this study introduces a novel approach that integrates the supply chain network for distant-water fisheries. This approach not only involves an integrated maritime location inventory routing problem (MLIRP) but also considers the identification of offshore fishing grounds based on geographic information system (GIS) techniques. The proposed model centers on critical decision variables, including selection of fishery production areas, strategic placement and sizing of perishable goods depots, and allocation of refrigerated vessels. Meanwhile, the model proposes two trade-off objective functions: one seeks to maximize the weighted coverage rate of fishery resource within selected production areas, while the other aims to minimize the total cost of the built network. To address the complex model, a method based on the k-means clustering and the multi-objective plant growth simulation algorithm (MO-PGSA) is adopted. Key elements, such as growth operators, dominant strength, crowding distance, and partially ordered sets, are involved to enhance algorithm performance. Finally, the effectiveness of the proposed model and method are discussed through numerical experiments based on the real-life case in the Spratly Islands.

Enhanced Artificial Bee Colony with Savings Algorithm for Inventory Routing Problem

Inventory Routing Problem is a critical component of Supply Chain Management, where it is a coordination of inventory management and transportation. It aims to balance the trade-off between transportation costs for delivering products and holding costs for maintaining inventory. Several real-world problems faced nowadays require effective optimization and logistical solutions, where this problem arises in various industries and has become increasingly complex. The problem addressed in this study is based on an automotive parts supply chain that consists of a depot, an assembly plant, a set of homogeneous capacitated vehicles, and multi-suppliers on a finite horizon with multi-periods. Artificial Bee Colony is a swarm intelligence algorithm that is based on the behaviour of bees in a colony, where information is shared through waggle dance. ABC consists of three phases, which are employed bee phase, onlooker bee phase, and scout bee phase. This study proposed an enhancement in the initialization phase and in onlooker bee phase of the ABC algorithm. Clarke Wright savings algorithm was implemented in the initialization phase to determine the best feasible delivery routes while minimizing the total transportation cost. 2-opt and 2-opt(asterisk) were used to improve the routes in the onlooker bee phase. Results showed that 7 better total cost were found out of 14 benchmark datasets when compared to the previous literature. The enhanced ABC algorithm obtained better results with 5.59 percent at most, which demonstrated the effectiveness of the algorithm.

An ALNS-based matheuristic algorithm for a multi-product many-to-many maritime inventory routing problem

In this paper, we propose an adaptive large neighborhood search-based matheuristic algorithm to solve a multi-product many-to-many maritime inventory routing problem. The problem addresses a short sea inventory routing problem that aims to find the best route and distribution plan for multiple products with a heterogeneous fleet of vessels through a network including several producers and customers. Each port can be visited a given number of times during the planning horizon, and the stock level for each product should lie within the predefined bound limits. The problem was introduced by Hemmati et al. (Eur J Oper Res 252:775–788, 2016). They developed a mixed integer programming formulation and proposed a matheuristic algorithm to solve the problem. Although their proposed algorithm worked well in terms of running time, it suffers from disregarding a part of the solution space. In this study, we propose a new matheuristic algorithm to find better solutions by exploring the entire solution space for the same problem. In our solution methodology, we split the variables into routing and non-routing variables. Then in an iterative process, we determine the values of the routing variables with an adaptive large neighborhood search algorithm, and we pass them as input to a penalized model which is a relaxed and modified version of the mathematical model introduced in Hemmati et al. (2016). The information from solving the penalized model, including the values of the non-routing variables, is then passed to the adaptive large neighborhood search algorithm for the next iteration. Several problem-dependent operators are defined. The operators use the information they get from the penalized model and focus on decreasing the penalty values. Computational results show up to 26% improvement in the quality of the solutions for the group of instances with a large feasible solution space. We get the optimal value for the remaining instances matched with the reported results.

A multi-stage stochastic programming approach for an inventory–routing problem considering life cycle

Food waste and proper methods to deal with it are one of the main challenges of supply chain network management. The majority of studies on how to use mathematical models in the supply chain have focused on goods that are at their peak of freshness as soon as they are produced and deteriorate over time. While some products experience an increase in value at the start of their life cycle, this value eventually reaches its maximum level, and after this point, these products experience a decline in value before being eliminated from the consumption cycle. The objective of this study is to develop a comprehensive inventory–routing model suitable for supply chain networks where products exhibit an increase and decrease in value over time. By considering the randomness and dynamic uncertainty of market demands and the fact that each period has effects on the next period, The proposed model employs a multi-stage stochastic programming (MSSP) approach. By doing so, the model ensures a balanced flow between different components of the network while considering nondeterministic demand under various scenarios that are shown in a tree of scenarios. The utilization of MSSP leads to more reliable solutions compared to deterministic models, making it possible for chain stores to make well-informed decisions in their inventory management and distribution strategies. Ultimately, this approach results in cost savings for chain stores handling such products. This research makes a significant contribution to the existing literature by demonstrating the effectiveness of the proposed model on actual data and highlighting the benefits of using stochastic programming in supply chain optimization.

Knowledge-based optimization algorithm for the inventory routing problem

AbstractThe Inventory Routing Problem (IRP) is a combinatorial optimization problem that combines routing decisions with inventory management. In this paper, an approach to solving the IRP is studied, which aims at using an external knowledge source (a known good solution or user interaction) to improve the results attained by an evolutionary algorithm solving an IRP instance. The proposed method improves the best solution found by the evolutionary algorithm by modifying schedules for some of the retailers according to those present in the known good solution or to schedules provided by a domain expert. The experiments shown that to improve the optimization results it suffices to perform a few repetitions of the knowledge import procedure. This observation motivates further research on user-interactive optimization algorithms for the IRP, because the number of interactions needed to improve the results can easily be handled by the user.

New benchmark instances for the inventory routing problem

The existing sets of benchmark instances for the inventory routing problem (IRP) have been beneficial for investigating and illustrating the properties of the problem. However, they possess certain features and design choices that are not necessarily representative of all real-world IRPs. Therefore, we propose a new collection of 270 real-world-like instances ranging from 10 to 200 customers. These instances vary in terms of the number of vehicles and their capacity, the length of the planning horizon, the demand structure, and the geographical distribution of customers. Transportation and inventory holding costs resemble costs found in practice. We present an instance space analysis showing that the new instances nicely complement the original instances. To derive lower and upper bounds for each instance, we present computational experiments with two high-quality solution methods: a matheuristic and an exact branch-and-cut method. The results confirm that the new set of instances is hard to solve with the proposed methods, and they demonstrate the need for developing new solution methods.

A Three-Front Parallel Branch-and-Cut Algorithm for Production and Inventory Routing Problems

Production and inventory routing problems consider a single-product supply chain operating under a vendor-managed inventory system. A plant creates a production plan and vehicle routes over a planning horizon to replenish its customers at minimum cost. In this paper, we present two- and three-index formulations, implement a branch-and-cut algorithm based on each formulation, and introduce a local search matheuristic-based algorithm to solve the problem. In order to combine all benefits of each algorithm, we design a parallel framework to integrate all three fronts, called the three-front parallel branch-and-cut algorithm (3FP-B&C). We assess the performance of our method on well-known benchmark instances of the inventory routing problem (IRP) and the production routing problem (PRP). The results show that our 3FP-B&C outperforms by far other approaches from the literature. For the 956 feasible small-size IRP instances, our method proves optimality for 746, being the first exact algorithm to solve all instances with up to two vehicles. 3FP-B&C finds 949 best known solutions (BKS) with 153 new BKS (NBKS). For the large-size set, our method provides two new optimal solutions (OPT), and finds 82% of BKS, being 70% of NBKS for instances with up to five vehicles. This result is more than twice the number of BKS considering all heuristic methods from the literature combined. Finally, our 3FP-B&C finds the best lower bounds (BLB) for 1,169/1,316 instances, outperforming all previous exact algorithms. On the PRP, our method obtained 278 OPT out of the 336 instances of benchmark set of small- and medium-size instances being 19 new ones in addition to 335 BKS (74 NBKS) and 313 BLB (52 new ones). On another set of PRP with medium- and large-size instances, our algorithm finds 1,105 BKS out of 1,440 instances with 584 NBKS. Besides that, our 3FP-B&C is the first exact algorithm to solve the instances with an unlimited fleet, providing the first lower bounds for this subset with an average optimality gap of 0.61%. We also address a very large-size instance set, the second exact algorithm to address this set, outperforming the previous approach by far. Finally, a comparative analysis of each front shows the gains of the integrated approach. History: This paper has been accepted for the Transportation Science Special Issue: DIMACS Implementation Challenge: Vehicle Routing. Funding: C. M. Schenekemberg was supported by the São Paulo Research Foundation (FAPESP) [Grant 2020/07145-8]. A. A. Chaves was supported by FAPESP [Grants 2018/15417-8 and 2016/01860-1] and Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grants 312747/2021-7 and 405702/2021-3]. L. C. Coelho was supported by the Canadian Natural Sciences and Engineering Research Council [Grant 2019-00094]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0261 .

A multi-objective solution framework for the assembly inventory routing problem considering supply risk and carbon offset policies

This study aims to provide novel insights into the multi-objective optimisation of an inbound assembly inventory routing problem (IRP) by considering customer demand uncertainty, stochastic supply failure risks, and a carbon offset policy. An inbound IRP network generally comprises several geographically dispersed suppliers, vehicle depots, and assembly plants. In this study, a new mixed-integer nonlinear optimisation model is formulated considering two objective functions: (i) minimising the total supply network cost and (ii) maximising a low-risk supplier priority function with practical constraints. A hybrid non-dominated sorting genetic algorithm-II was developed to obtain near-optimal Pareto solutions for various small, medium, and large IRP instances. The Pareto solutions were compared with the efficient solution obtained using the ε-constraint method. Finally, the best Pareto solution was obtained using the multi-criteria decision-making technique. The results indicate that implementing supply risk-mitigation strategies leads to higher overall supply network costs and carbon emissions. However, a sensitivity analysis based on factorial simulation experiments indicates that a supply risk-mitigation strategy is advantageous if component prices are low and supply capacity, fuel price, and demand variations are high. In addition, the lower the demand variation, the lower the expected overall network cost and carbon emissions.

On the zero-inventory-ordering policy in the inventory routing problem

The Inventory Routing Problem (IRP) aims at determining the best distribution plan of a certain commodity from a supplier to a set of customers over a given planning horizon. Customers face a per period consumption and the plan has to be such that they can always satisfy it. The aim is to minimize the total cost of the distribution plan, which is given by the sum of routing and inventory holding cost. A replenishment strategy that has become common in the recent literature is the Maximum Level (ML) strategy, where no restriction is imposed on when the customers are visited and what the quantity delivered is, provided that a maximum inventory level at each customer (corresponding to the customer′s warehouse capacity) is not exceeded. This strategy is highly flexible and this clearly provides cost advantages. However, it might also create inconveniences to customers, who might receive visits when their inventory level is still relatively high. Towards addressing this issue, we study in this paper the Zero-Inventory-Ordering (ZIO) replenishment strategy for the IRP, where customers can be served only when their inventory level is zero. The aim is to analyze the impact of a policy which is more customer-orientedthan the ML. The analysis is made in terms of advantages from the customers′ perspective and disadvantages from the system perspective, i.e., increase of the total cost. We propose a formulation based on two-commodity flow variables, and strengthen it through new valid inequalities tailored for our problem as well as with valid inequalities inherited from the literature on the IRP. We develop branch-and-cut algorithms and experimentally compare the ZIO and ML policies on benchmark IRP instances. The results show that the application of the ZIO policy allows to reduce the inventory costs at the customers without substantially increasing, or even decreasing, the number of visits to them. This comes at the expense of an increase of the total costs. Results also show that the increase in total cost is inversely proportional to the relative weight of the inventory costs at the customers. More precisely, inventory costs at customers are decreased by more than 20% on average while total cost increases, on average, by 17.6% when the inventory costs are high and of 9.2% when inventory costs are low. In addition, we generated new sets of instances in which inventory costs are more aligned with practical applications with respect to what happens in the benchmark IRP instances. Results show how the ZIO policy consistently provides solutions where the inventory cost to customers is lower than the one associated with the ML policy. Also, the gap in total cost reduces when the inventory cost at customers increases.

A branch-and-cut embedded matheuristic for the inventory routing problem

This paper presents an improved version of the solution method that won the inventory routing problem track of the 12th DIMACS Implementation Challenge. The solution method is a branch-and-cut embedded matheuristic where a matheuristic is called every time a new primal solution is found in a branch-and-cut method. The matheuristic consists of a construction heuristic and an improvement heuristic. The construction heuristic uses a giant tour method and a shifting assignments method to generate a set of promising routes which, in turn, are combined into a feasible solution to the problem by solving a route-based mathematical program. The improvement heuristic then solves a series of extended route-based mathematical programs where clusters of customers may be inserted and/or removed from the routes of the initial feasible solution. We have, to the best of our knowledge, gathered all detailed results from previously published methods for the inventory routing problem and made this overview available online. Compared with these results, the proposed method found the best-known solution for 741 out of 878 multi-vehicle inventory routing instances, where 247 of them are strictly better than the previously best-known solutions. Furthermore, we prove optimality for 458 of these solutions. The proposed method is also able to find the best-known solution for 116 out of 226 benchmark instances for the split delivery vehicle routing problem, and improve three best-known solutions from the CVRPlib for the capacitated vehicle routing problem.

The inventory routing problem with split deliveries

AbstractWe study the benefit of introducing split deliveries in the inventory routing problem (IRP), both when the order‐up‐to level (OU) and the maximum level replenishment policies are applied. We first propose a mathematical formulation and solve it by implementing a branch‐and‐cut algorithm. Then, we carry out a worst‐case analysis to show the cost increase we have in the worst case by using unsplit deliveries instead of split deliveries, both for the OU and the maximum‐level replenishment policies. Extensive computational results on benchmark instances allow us to evaluate the benefit of introducing split deliveries. Finally, a sensitivity analysis on customer demands, initial inventory levels, maximum inventory levels and distance to the depot allows us to understand the instance features that make split deliveries effective in IRPs.

The Characteristics of Demand Rates in Inventory Routing Problem

The Characteristics of Demand Rates in Inventory Routing Problem